We define directional Robin constants associated to a compact subset of an algebraic curve. We show that these constants satisfy an upper envelope formula given by polynomials. We use this formula to relate the directional Robin constants of the set to its directional Chebyshev constants. These constants can be used to characterize algebraic curves on which the Siciak-Zaharjuta extremal function is harmonic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-1,
author = {Jesse Hart and Sione Ma`u},
title = {Chebyshev and Robin constants on algebraic curves},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {101-121},
zbl = {06487228},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-1}
}
Jesse Hart; Sione Ma`u. Chebyshev and Robin constants on algebraic curves. Annales Polonici Mathematici, Tome 113 (2015) pp. 101-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-1/